Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}7x+6y &= -6 \\ 7x+8y &= 6\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $7x = -8y+6$ Divide both sides by $7$ to isolate $x$ $x = {-\dfrac{8}{7}y + \dfrac{6}{7}}$ Substitute this expression for $x$ in the first equation. $7({-\dfrac{8}{7}y + \dfrac{6}{7}}) + 6y = -6$ $-8y + 6 + 6y = -6$ Simplify by combining terms, then solve for $y$ $-2y + 6 = -6$ $-2y = -12$ $y = 6$ Substitute $6$ for $y$ in the top equation. $7x+6( 6) = -6$ $7x+36 = -6$ $7x = -42$ $x = -6$ The solution is $\enspace x = -6, \enspace y = 6$.